With the new Zelda trailer, I've determined I really want to try beating all of the Zelda games. Only one I've ever played is Ocarina of Time, which I absolutely loved. My only slight issue is I definitely had to use a guide a time or two since I tend to get annoyed if I have to run around hopelessly for too terribly long.

Backstory aside, I'm wondering if anybody has advice on whether there is a certain order I should be playing the games in (note I intend on replaying OoT), or for that matter, any games I should completely avoid? The handhelds are certainly easier for me to play since the N64/WiiU tv is shared with roommates for the time being. My understanding is also that the Four Swords games aren't the greatest single player experience. Is Tri Force similar to this too?

I did start up on Oracle of Ages today and got about halfway through it (absoutely wonderful game).

Well, A Link Between Worlds is awesome, really addictive, best game of 3DS imo, so if you are looking for a handheld Zelda look no further.

Since this need to play Zelda comes because the hype of the new one I would higly recomend you Wind Waker HD, is the most similar game on the series to BotW and is a glorious one.

Honestly, my advice would be go back and start with the first NES Legend of Zelda, because it's the most open, and basic, and it's a perfect intro to the series. From there, I'd suggest A Link to the Past on SNES, and Link's Awakening (my personal fav.) on GameBoy. Great, great games.

Ocarina of Time seems to be the popular pick for "best Zelda game ever", but honestly, while it IS a good game, it hasn't aged super well, and I think it was always overrated. Amazing for it's TIME, yes, but hardly amazing today. I'd say give Ocarina a spin, yet at the same time, I'd say that Twilight Princess is a very similar experience to Ocarina, except with more to it and more or less better everything. At least in my opinion. It starts slow, but the overall experience is worth it.

DO NOT play Skyward Sword. Motion controls ruined the whole game. Ocarina is great, Majora is great... any Zelda game without a need of a stylus or motion controls are great.    

I'd recommend avoiding both Four Swords games, and Tri Force Heroes if you plan on playing the single player by yourself.

Other than that, I'd highly recommend to you Wind Waker HD and Twilight Princess HD, they are truly incredible games. Great big shout out to A Link Between Worlds on 3DS, definitely one of the best 2D Zelda games, if not the best already.

Buy the skyward sword special edition pack with the golden controller. It works very good and i never had issues with it. Really enjoyable experience like any other zelda

My personal start with the series was Wind Waker. Great sense of adventure, was fun without being too challenging, had memorable characters and humor, and was overall a very pleasant experience. My personal favorite is Twilight Princess HD. Loved the combat, atmosphere, story, dungeon designs, and the boss fights. No it isn't super challenging, but it's always fun and has a great sense of epicness. Skyward Sword definitely is the best written with the best cast, just be ready to get used to those motion controls. Still enjoy it a lot, Lanaryu is a super cool region.

I would recommend Twilight Princess HD (SPECIFICALLY that version) or Wind Waker HD for your next one. I don't recommend the original Zelda as it is a guide game and those stopped being a thing for good reasons. Heard nothing but good about Link to the Past though.

Then why would you recommend this game for him to play first then? Since he wants to beat them all ;)

I recommend Wind Waker HD, Twilight Princess HD, Skyward Sword, Ocarina 3D, and A Link Between Worlds. I started with Ocarina like you and found going back to Zelda 1, 2, or A Link to the Past to be unappealing. I've tried all the Zelda games, but the console 3D Zeldas (and A Link Between Worlds...seriously awesome) are the ones that I've always enjoyed the most. And again, I think starting with Ocarina is the reason for that. Majora's Mask has been the exception for me as the time-limit (three-day system) makes the game really difficult for me to enjoy. I like to take my time exploring and appreciating game worlds and Majora's Mask just isn't really built for that, even if you can reset the time over and over easily enough and slow it down, it just isn't a Zelda I can get into. Similarly, I didn't really like Phantom Hourglass because you do a stupid timed dungeon repeatedly throughout the game. Spirit Tracks is better, though that game has some of its own issues (incredible soundtrack though!). So if anything I'd say to avoid the DS Zeldas. I did enjoy Minish Cap, and will be trying to give the Oracle games another chance since I got them on sale. But yeah, if you like Ocarina, stick with the 3D Zeldas first if possible (and A Link Between Worlds). And don't listen to the Skyward Sword haters. Sure, motion controls may not be for everybody, and if that's you then by all means--avoid it. But I won't let somebody say the controls don't work, because they've always worked flawlessly for me and I've enjoyed that game every time I've played it. Its beautiful, brilliant, and creative.

If you don't like 'running around hopelessly' the games you will enjoy the most are Skyward Sword, Twilight Princess, and Wind Waker. The first Zelda does not give you directions on how to proceed and leaves it to you to discover the dungeons and secrets on your own, and the second is radically different from the rest of the series and makes Dark Souls look like a Kirby game when it comes to difficulty.

If you won't be turned off by that then just play the games in the order they came out. If you are turned off then play WW, TP, and SS first and the start the 2d Zeldas with A Link Between Worlds and Minish Cap, as those are the most accessible of the classic 2d style games.

I first played Ocarina of time and Twilight Princess at the same time in 2007, and found that TP was a much better designed game. Going back to the older 2d games is not easy when you play them after the 3d games.